Problem: Calculate the quotient below and give your answer in scientific notation. ${\dfrac{4.16\times 10^{-5}}{8.0\times 10^{-4}}} =\ ?$
Explanation: Start by collecting the significands and exponents. $ {\dfrac {{4.16} \times {10^{-5}}} {{8.0} \times {10^{-4}}} = {\dfrac{4.16}{8.0}} \times {\dfrac{10^{-5}}{10^{-4}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.52} \times {10^{-5 \,-\, -4}}$ $= {0.52} \times {10^{-1}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.52}$ is the same as ${5.2 \div 10}$, or ${5.2 \times 10^{-1}}$. $ = {5.2 \times 10^{-1}} \times {10^{-1}} $ $ = 5.2 \times 10^{{-1} + {-1}} $ $= 5.2\times 10^{-2}$